MicrowaveandMillimeterWaveTechnologies:ModernUWBantennasandequipment232 shown in Figure 3, where the beampatterns of the omnidirectional and the directive cases for θ 0 =0 are shown as an example. -1 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0 -35 -30 -25 -20 -15 -10 -5 0 u-u 0 dB Omnidirectional sensor array Directive sensor array Fig. 3. Sensor directivity effect vs. |u-u 0 | In order to characterize absolute variation of sidelobe levels, ΔSLL i has been defined: )º0()º60( 00    iii SLLSLLSLL (2) Table 1 shows the absolute variation of the 8 first sidelobes located on the left of the mainlobe. It can be observed that moving away from the mainlobe (increasing index i), the variation of the sidelobe level increases. For the fifth sidelobe, ΔSLL is greater than 3dB. i 1 2 3 4 5 6 7 8 ΔSLL i 1.51 1.67 2.16 2.63 3.11 3.65 4.25 5.16 Table 1. ΔSLL i (dB) for the 8 sidelobes on the left of the mainlobe This section continues with detailed studies for several sidelobe levels, where dependences on the steering angle, sensor spacing and directive factor C are analyzed. 2.1 First Sidelobe Level (SLL 1 ) SLL 1 Sensitivity vs. steering angle Figure 4 shows that increasing steering angles produce higher first sidelobe levels, at the left of the mainlobe. For small steering angles, the first sidelobe level is below the omnidirectional case, but with greater angles the sidelobe level exceeds the omnidirectional one. The reason of this behaviour is that pointing the beam more and more to the right, i.e. increasing the steering angle, makes beampattern values on the left of the mainbeam be affected by lower and lower sensor directivity values, as it is showed in Figure 5. The effect of sensor directivity over the first sidelobe can vary its level in 1.52dB. 0 10 20 30 40 50 60 -13.5 -13 -12.5 -12  0 (º) SLL 1 (dB) Omnidirectional sensor array Directive sensor array Fig. 4. Left SLL 1 vs. Steering angle 0 0.2 0.4 0.6 0.8 1 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 0 0.2 0.4 0.6 0.8 1 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 a) b) 0 0.2 0.4 0.6 0.8 1 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 0 0.2 0.4 0.6 0.8 1 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 0 0.2 0.4 0.6 0.8 1 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 0 0.2 0.4 0.6 0.8 1 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 0 0.2 0.4 0.6 0.8 1 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 0 0.2 0.4 0.6 0.8 1 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 a) b) Fig. 5. Sensor directivity effect on first sidelobe level. Spacing=λ/2. a) θ 0 =0º, b) θ 0 =20º SLL 1 Sensitivity vs. sensor spacing: This first sidelobe level analysis is extended with a study of sensor directivity influence on array beampattern with regard to sensor spacing. This spacing is varied between 0.25λ and 1λ. Directive factor (C) is fixed to 1. Figure 6 shows this influence with regard to sensor spacing. It can be observed that an increase on sensor spacing deals to a SLL 1 decrease. Analysisofdirectivesensorinuenceonarraybeampatterns 233 shown in Figure 3, where the beampatterns of the omnidirectional and the directive cases for θ 0 =0 are shown as an example. -1 -0.9 -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.2 -0.1 0 -35 -30 -25 -20 -15 -10 -5 0 u-u 0 dB Omnidirectional sensor array Directive sensor array Fig. 3. Sensor directivity effect vs. |u-u 0 | In order to characterize absolute variation of sidelobe levels, ΔSLL i has been defined: )º0()º60( 00        iii SLLSLLSLL (2) Table 1 shows the absolute variation of the 8 first sidelobes located on the left of the mainlobe. It can be observed that moving away from the mainlobe (increasing index i), the variation of the sidelobe level increases. For the fifth sidelobe, ΔSLL is greater than 3dB. i 1 2 3 4 5 6 7 8 ΔSLL i 1.51 1.67 2.16 2.63 3.11 3.65 4.25 5.16 Table 1. ΔSLL i (dB) for the 8 sidelobes on the left of the mainlobe This section continues with detailed studies for several sidelobe levels, where dependences on the steering angle, sensor spacing and directive factor C are analyzed. 2.1 First Sidelobe Level (SLL 1 ) SLL 1 Sensitivity vs. steering angle Figure 4 shows that increasing steering angles produce higher first sidelobe levels, at the left of the mainlobe. For small steering angles, the first sidelobe level is below the omnidirectional case, but with greater angles the sidelobe level exceeds the omnidirectional one. The reason of this behaviour is that pointing the beam more and more to the right, i.e. increasing the steering angle, makes beampattern values on the left of the mainbeam be affected by lower and lower sensor directivity values, as it is showed in Figure 5. The effect of sensor directivity over the first sidelobe can vary its level in 1.52dB. 0 10 20 30 40 50 60 -13.5 -13 -12.5 -12  0 (º) SLL 1 (dB) Omnidirectional sensor array Directive sensor array Fig. 4. Left SLL 1 vs. Steering angle 0 0.2 0.4 0.6 0.8 1 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 0 0.2 0.4 0.6 0.8 1 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 a) b) 0 0.2 0.4 0.6 0.8 1 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 0 0.2 0.4 0.6 0.8 1 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 0 0.2 0.4 0.6 0.8 1 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 0 0.2 0.4 0.6 0.8 1 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 0 0.2 0.4 0.6 0.8 1 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 0 0.2 0.4 0.6 0.8 1 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 a) b) Fig. 5. Sensor directivity effect on first sidelobe level. Spacing=λ/2. a) θ 0 =0º, b) θ 0 =20º SLL 1 Sensitivity vs. sensor spacing: This first sidelobe level analysis is extended with a study of sensor directivity influence on array beampattern with regard to sensor spacing. This spacing is varied between 0.25λ and 1λ. Directive factor (C) is fixed to 1. Figure 6 shows this influence with regard to sensor spacing. It can be observed that an increase on sensor spacing deals to a SLL 1 decrease. MicrowaveandMillimeterWaveTechnologies:ModernUWBantennasandequipment234 0 10 20 30 40 50 60 -13.4 -13.2 -13 -12.8 -12.6 -12.4 -12.2 -12 -11.8 -11.6 -11.4  0 (º) SLL 1 (dB) 0.25  0.5  0.75  1  Fig. 6. SLL 1 vs. Steering angle (θ 0 ) for several sensor spacing. C=1. 0 0.2 0.4 0.6 0.8 1 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 0 0.2 0.4 0.6 0.8 1 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 0 0.2 0.4 0.6 0.8 1 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 0 0.2 0.4 0.6 0.8 1 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 a) b) d)c) 0 0.2 0.4 0.6 0.8 1 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 0 0.2 0.4 0.6 0.8 1 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 0 0.2 0.4 0.6 0.8 1 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 0 0.2 0.4 0.6 0.8 1 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 0 0.2 0.4 0.6 0.8 1 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 0 0.2 0.4 0.6 0.8 1 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 0 0.2 0.4 0.6 0.8 1 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 0 0.2 0.4 0.6 0.8 1 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 0 0.2 0.4 0.6 0.8 1 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 0 0.2 0.4 0.6 0.8 1 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 a) b) d)c) Fig. 7. Sensor directivity effect on first sidelobe level. C=1. a) Spacing=λ/2 and θ 0 =0º; b) Spacing=λ/2 and θ 0 =20º; c) Spacing=0.25λ and θ 0 =0º; d) Spacing=0.25λ and θ 0 =20º The reason of this behaviour is that increasing sensor spacing makes a compression of the beampattern. Figure 7 shows how the first sidelobe is closer and closer to the mainbeam, reducing the difference between the directivity values that affects each of these lobes (first sidelobe and mainlobe). The variation of SLL 1 (ΔSLL 1 ) is inversely proportional to sensor spacing, as it can be observed in Figure 8. The sensitivity of ΔSLL 1 versus sensor spacing is lower than the one on steering angle. This effect must be taken into account, since it can increase sidelobe level between 0.68dB and 1.81dB, i.e. a 1.13dB variation. 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.8 1 1.2 1.4 1.6 1.8 Spacing (  )  SLL 1 (dB) Fig. 8. ΔSLL 1 vs. Sensor spacing SLL 1 Sensitivity vs. Directive factor C SLL 1 analysis is finished off with a study of sensor directivity influence on the array beampattern with regard to sensor directive factor (C). This directivity factor is varied between 1 and 0.25. Sensor spacing is fixed to 0.5λ. Figure 9 shows this influence. It can be observed that decreasing directive factor, i.e. using more directive sensors, increases SLL 1 . The reason of this behaviour is that sharper sensor directivity deals to a larger difference between the directivity values that affect first sidelobe and mainlobe, as Figure 10 shows. The variation of SLL 1 (ΔSLL 1 ), is inversely proportional to the directive factor, as it can be observed in Figure 11. The sensitivity of SLL 1 versus directive factor is lower than the sensitivity versus sensor spacing. In this case, the effect can be increased from 1.11dB to 2.03dB, i.e. a 0.92dB variation. These SLL 1 analyses show that SLL 1 is less sensitive to directive factor variations than to spacing and steering angle ones. The highest sensitivity is shown for the steering angle. All these analyses have been done for positive steering angles. In the case of negative steering angles values, the behaviour would be the symmetric one. Analysisofdirectivesensorinuenceonarraybeampatterns 235 0 10 20 30 40 50 60 -13.4 -13.2 -13 -12.8 -12.6 -12.4 -12.2 -12 -11.8 -11.6 -11.4  0 (º) SLL 1 (dB) 0.25  0.5  0.75  1  Fig. 6. SLL 1 vs. Steering angle (θ 0 ) for several sensor spacing. C=1. 0 0.2 0.4 0.6 0.8 1 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 0 0.2 0.4 0.6 0.8 1 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 0 0.2 0.4 0.6 0.8 1 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 0 0.2 0.4 0.6 0.8 1 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 a) b) d)c) 0 0.2 0.4 0.6 0.8 1 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 0 0.2 0.4 0.6 0.8 1 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 0 0.2 0.4 0.6 0.8 1 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 0 0.2 0.4 0.6 0.8 1 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 0 0.2 0.4 0.6 0.8 1 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 0 0.2 0.4 0.6 0.8 1 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 0 0.2 0.4 0.6 0.8 1 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 0 0.2 0.4 0.6 0.8 1 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 0 0.2 0.4 0.6 0.8 1 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 0 0.2 0.4 0.6 0.8 1 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 a) b) d)c) Fig. 7. Sensor directivity effect on first sidelobe level. C=1. a) Spacing=λ/2 and θ 0 =0º; b) Spacing=λ/2 and θ 0 =20º; c) Spacing=0.25λ and θ 0 =0º; d) Spacing=0.25λ and θ 0 =20º The reason of this behaviour is that increasing sensor spacing makes a compression of the beampattern. Figure 7 shows how the first sidelobe is closer and closer to the mainbeam, reducing the difference between the directivity values that affects each of these lobes (first sidelobe and mainlobe). The variation of SLL 1 (ΔSLL 1 ) is inversely proportional to sensor spacing, as it can be observed in Figure 8. The sensitivity of ΔSLL 1 versus sensor spacing is lower than the one on steering angle. This effect must be taken into account, since it can increase sidelobe level between 0.68dB and 1.81dB, i.e. a 1.13dB variation. 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.8 1 1.2 1.4 1.6 1.8 Spacing (  )  SLL 1 (dB) Fig. 8. ΔSLL 1 vs. Sensor spacing SLL 1 Sensitivity vs. Directive factor C SLL 1 analysis is finished off with a study of sensor directivity influence on the array beampattern with regard to sensor directive factor (C). This directivity factor is varied between 1 and 0.25. Sensor spacing is fixed to 0.5λ. Figure 9 shows this influence. It can be observed that decreasing directive factor, i.e. using more directive sensors, increases SLL 1 . The reason of this behaviour is that sharper sensor directivity deals to a larger difference between the directivity values that affect first sidelobe and mainlobe, as Figure 10 shows. The variation of SLL 1 (ΔSLL 1 ), is inversely proportional to the directive factor, as it can be observed in Figure 11. The sensitivity of SLL 1 versus directive factor is lower than the sensitivity versus sensor spacing. In this case, the effect can be increased from 1.11dB to 2.03dB, i.e. a 0.92dB variation. These SLL 1 analyses show that SLL 1 is less sensitive to directive factor variations than to spacing and steering angle ones. The highest sensitivity is shown for the steering angle. All these analyses have been done for positive steering angles. In the case of negative steering angles values, the behaviour would be the symmetric one. MicrowaveandMillimeterWaveTechnologies:ModernUWBantennasandequipment236 0 10 20 30 40 50 60 -13.5 -13 -12.5 -12 -11.5 -11  0 (º) SLL 1 (dB) C=1 C=0.75 C=0.5 C=0.25 Fig. 9. SLL 1 vs. Steering angle (θ 0 ) for several directive factors (C). Spacing=λ/2. 0 0.2 0.4 0.6 0.8 1 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 0 0.2 0.4 0.6 0.8 1 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 Fig. 10. Sensor directivity effect on first sidelobe level. Spacing=λ/2. C=1 ( __ ), C=0.25 ( - - ) 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 Directive factor C  SLL 1 dB Fig. 11. ΔSLL 1 vs. Directive factor C 2.2 Sidelobe Average Level ( SLL ) The analysis of the average sidelobe level ( SLL ) is similar to the analysis of the first sidelobe level. A sidelobe average level that calculates the average of the first 8 sidelobes on the left of the mainlobe has been taken in consideration. This average level of an array formed by omnidirectional sensors is constant. Figure 12 shows that, an increase in steering angle causes an increase in SLL . Firstly, the average level values for the directional case are below the values of the omnidirectional case, but with an increasing steering angle, average level values of the directional case are over the omnidirectional ones. This average level has a variation ( SLL ) of 3.75dB. The analyses of the SLL sensibility versus sensor spacing and directive factor (C), have been made in the same way than the ones shown for SLL 1 . In this case, an increase on the spacing and/or on the directive factor, also means a decrease of SLL , as it can be observed in Figures 13 and 14. For this sidelobe level, the sensitivity of SLL versus sensor spacing is also lower than the one versus steering angle. Despite this sensitivity is lower, it must be taken into consideration, since it can increase average sidelobe level between 4.48dB and 6.51dB, i.e. a 2.17dB variation. The sensitivity of SLL versus directive factor is also lower than the sensitivity versus steering angle. In this case, the effect can be increased from 5.52dB to 7.60dB, i.e. a 2.08dB variation. These analyses show that SLL is more sensitive to directive factor variations than to spacing and steering angle ones. The highest sensitivity, as in the SLL 1 analysis, is shown for the steering angle. Analysisofdirectivesensorinuenceonarraybeampatterns 237 0 10 20 30 40 50 60 -13.5 -13 -12.5 -12 -11.5 -11  0 (º) SLL 1 (dB) C=1 C=0.75 C=0.5 C=0.25 Fig. 9. SLL 1 vs. Steering angle (θ 0 ) for several directive factors (C). Spacing=λ/2. 0 0.2 0.4 0.6 0.8 1 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 0 0.2 0.4 0.6 0.8 1 -20 -18 -16 -14 -12 -10 -8 -6 -4 -2 0 Fig. 10. Sensor directivity effect on first sidelobe level. Spacing=λ/2. C=1 ( __ ), C=0.25 ( - - ) 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2 Directive factor C  SLL 1 dB Fig. 11. ΔSLL 1 vs. Directive factor C 2.2 Sidelobe Average Level ( SLL ) The analysis of the average sidelobe level ( SLL ) is similar to the analysis of the first sidelobe level. A sidelobe average level that calculates the average of the first 8 sidelobes on the left of the mainlobe has been taken in consideration. This average level of an array formed by omnidirectional sensors is constant. Figure 12 shows that, an increase in steering angle causes an increase in SLL . Firstly, the average level values for the directional case are below the values of the omnidirectional case, but with an increasing steering angle, average level values of the directional case are over the omnidirectional ones. This average level has a variation ( SLL ) of 3.75dB. The analyses of the SLL sensibility versus sensor spacing and directive factor (C), have been made in the same way than the ones shown for SLL 1 . In this case, an increase on the spacing and/or on the directive factor, also means a decrease of SLL , as it can be observed in Figures 13 and 14. For this sidelobe level, the sensitivity of SLL versus sensor spacing is also lower than the one versus steering angle. Despite this sensitivity is lower, it must be taken into consideration, since it can increase average sidelobe level between 4.48dB and 6.51dB, i.e. a 2.17dB variation. The sensitivity of SLL versus directive factor is also lower than the sensitivity versus steering angle. In this case, the effect can be increased from 5.52dB to 7.60dB, i.e. a 2.08dB variation. These analyses show that SLL is more sensitive to directive factor variations than to spacing and steering angle ones. The highest sensitivity, as in the SLL 1 analysis, is shown for the steering angle. MicrowaveandMillimeterWaveTechnologies:ModernUWBantennasandequipment238 0 10 20 30 40 50 60 -24 -23.5 -23 -22.5 -22 -21.5 -21 -20.5 -20 -19.5  0 (º) SLL average (dB) Omnidirectional sensor array Directive sensor array Fig. 12. SLL vs. Steering angle 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 4.5 5 5.5 6 6.5 Spacing (  )  SLL average (dB) Fig. 13. SLL vs. Sensor spacing 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 5.6 5.8 6 6.2 6.4 6.6 6.8 7 7.2 7.4 7.6 Directive factor C  SLL average (dB) Fig. 14. SLL vs. Directive Factor C 2.3 Maximum Sidelobe Level (SLL max ) Lastly, maximum sidelobe level (SLL max ), which is related with grating lobes, is analysed. Due to the appearance of grating lobes depends on sensor spacing, the influence of this spacing on the variation of SLL max and steering angle is studied. Figure 15 shows that an increase of steering angle means an increase of SLL max for all spacing. For spacing greater than λ/2, there are two different behaviours: (a) A first one, with SLL max around -13dB that grows up slowly with increasing steering angle. (b) A second one, where SLL max suffers a quite abrupt increase. This increase indicates the existence of grating lobes. For λ spacing, the behaviour is again unique, because there are grating lobes for all the steering angles. Comparing Figures 15 and 16, where SLL max performance for an omnidirectional sensor array is shown, it can be observed that the sensor directive response makes grating lobes appearance more gradual and less abrupt than in the omnidirectional case. This is an improvement in array performance, but it is also a problem because it can be even greater than the mainlobe. Analysisofdirectivesensorinuenceonarraybeampatterns 239 0 10 20 30 40 50 60 -24 -23.5 -23 -22.5 -22 -21.5 -21 -20.5 -20 -19.5  0 (º) SLL average (dB) Omnidirectional sensor array Directive sensor array Fig. 12. SLL vs. Steering angle 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 4.5 5 5.5 6 6.5 Spacing (  )  SLL average (dB) Fig. 13. SLL vs. Sensor spacing 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 5.6 5.8 6 6.2 6.4 6.6 6.8 7 7.2 7.4 7.6 Directive factor C  SLL average (dB) Fig. 14. SLL vs. Directive Factor C 2.3 Maximum Sidelobe Level (SLL max ) Lastly, maximum sidelobe level (SLL max ), which is related with grating lobes, is analysed. Due to the appearance of grating lobes depends on sensor spacing, the influence of this spacing on the variation of SLL max and steering angle is studied. Figure 15 shows that an increase of steering angle means an increase of SLL max for all spacing. For spacing greater than λ/2, there are two different behaviours: (a) A first one, with SLL max around -13dB that grows up slowly with increasing steering angle. (b) A second one, where SLL max suffers a quite abrupt increase. This increase indicates the existence of grating lobes. For λ spacing, the behaviour is again unique, because there are grating lobes for all the steering angles. Comparing Figures 15 and 16, where SLL max performance for an omnidirectional sensor array is shown, it can be observed that the sensor directive response makes grating lobes appearance more gradual and less abrupt than in the omnidirectional case. This is an improvement in array performance, but it is also a problem because it can be even greater than the mainlobe. MicrowaveandMillimeterWaveTechnologies:ModernUWBantennasandequipment240 0 10 20 30 40 50 60 -14 -12 -10 -8 -6 -4 -2 0 2 4  0 (º) SLL max (dB) 0.25  0.5  0.6  0.75  0.9  1  Fig. 15. SLL max vs. Steering angle for several sensor spacing. C=1. Directive sensor array 0 10 20 30 40 50 60 -14 -12 -10 -8 -6 -4 -2 0 2 4  0 (º) SLL max (dB) 0.25  0.5  0.6  0.75  0.9  1  Fig. 16 SLL max vs. Steering angle for several sensor spacing. Omnidirectional sensor array 3. Conclusions This paper shows that using arrays with directive sensors makes the invariance hypothesis no longer valid. Sidelobe level increments around 5dB can be observed if directive sensors are used. This effect can be increased depending on the sensor spacing and the directive factor. In Table 2, 1 SLL and SLL versus steering angle, spacing and directive factor relations are shown. Sidelobes are more sensitive to steering angle variation than to spacing and directive factor variation. SLL is more sensitive to parameter variation than SLL 1 , because SLL includes effects on several sidelobes, and these effects are larger in sidelobes which are more distant from the main lobe. SLL is also more sensitive because it includes grating lobes effect. This effect is also included in maximum sidelobe level. Sensor directivity produces a more gradual appearance of greater grating lobes. 1 SLL  [dB] SLL [dB] Steering angle 1.51 3.22 Sensor spacing 1.13 2.17 Directive factor (C) 0.92 2.08 Table 2. 1 SLL and SLL vs. steering angle, spacing and directive factor (C) The research has been realized for sensors whose directive response is a cardioids function, but it can be extended as a future work to any other type of directive response. It can be also extended to random arrays, because they are influenced by the sensor directive response. 4. References A. Akdagli, and K. Guney (2003). Shaped-Beam Pattern Synthesis of Equally and Unequally Spaced Linear Antenna Arrays Using a Modified Tabu Search Algorithm, Microwave and Optical Technology Letters, Vol. 36, No. 1, (Jan. 2003) 16-20, ISSN 0895- 2477 V. Agrawal and Y. Lo (1972). Mutual coupling in phased arrays of randomly spaced antennas, IEEE Transactions on Antennas and Propagation, Vol. AP-20, No. 3, (May 1972) 288-295, ISSN 1045-9243 J. Bae, K. Kim, and C. Pyo (2005). Design of Steerable Linear and Planar Array Geometry with Non-uniform Spacing for Side-Lobe Reduction, IEICE Transactions on Communications, Vol. E88-B, No. 1, (Jan. 2005) 345-357, ISSN 0916-8516 M. Brandstein, and D. Ward (2001). Microphone Arrays. Signal Processing Techniques and Applications, Springer-Verlag, ISBN 3-540-41953-5, Berlin M. Bray, D. Werner, D. Boeringer, and D. Machuga (2002). Optimization of Thinned Aperiodic Linear Phased Arrays Using Genetic Algorithms to Reduce Grating Lobes During Scanning, IEEE Transactions on Antennas and Propagation, Vol. 50, No. 12, (Dec. 2002) 1732-1742, ISSN 1045-9243 B. Feng, and Z. Chen (2004). Optimization of Three Dimensional Retrodirective Arrays, Proceedings of the IEEE 3rd Annual Communication Networks and Services Research Conference 2005, pp. 80-83, ISBN 0-7695-2333-1, Halifax (Nova Scotia, Canada), May 2005, Halifax R. Harrington (1961). Sidelobe reduction by nonuniform element spacing, IRE Transactions on Antennas and Propagation, Vol. 9, No. 2, (Mar. 1961) 187-192, ISSN 0096-1973 [...]... nonuniform element spacing, IRE Transactions on Antennas and Propagation, Vol 9, No 2, (Mar 196 1) 187- 192 , ISSN 0 096 - 197 3 242 Microwave and Millimeter Wave Technologies: Modern UWB antennas and equipment R Haupt ( 199 4) Thinned arrays using genetic algorithms, IEEE Transactions on Antennas and Propagation, Vol 42, No 7, (May 199 4) 99 3 -99 9, ISSN 1045 -92 43 B Kumar, and G Branner (2005) Generalized Analytical... structure of EPON 260 Microwave and Millimeter Wave Technologies: Modern UWB antennas and equipment Many research works have been done to realize RoF system with distributed BSs incorporating Wavelength Division Multiplexing (WDM) (Stöhr et al., 199 8; Griffin et al., 199 9) Compared to incorporating TDM, a RoF system based on WDM does not need complex protocols to handle data and can make the structure... al., 199 2) 246 Microwave and Millimeter Wave Technologies: Modern UWB antennas and equipment Fig 4 The usage of MZM as external modulator It can be seen that a single laser source is required together with a MZM By biasing the MZM at Vpi, the half -wave voltage of MZM, the optical carrier at center wavelength will be suppressed The beat of upper and lower 1st side-modes will yield required mm -wave signal,... Synthesis of Equally and Unequally Spaced Linear Antenna Arrays Using a Modified Tabu Search Algorithm, Microwave and Optical Technology Letters, Vol 36, No 1, (Jan 2003) 16-20, ISSN 0 895 2477 V Agrawal and Y Lo ( 197 2) Mutual coupling in phased arrays of randomly spaced antennas, IEEE Transactions on Antennas and Propagation, Vol AP-20, No 3, (May 197 2) 288- 295 , ISSN 1045 -92 43 J Bae, K Kim, and C Pyo (2005)... terms represent the IF side-bands centered at the (2n-1) th harmonics of RF signal If n=5, the 9th harmonics of RF signal are expressed as F9  2 REc {J 9 ( 2  ) sin (9 s t   )  J 0 ( ) J 9 (  ) cos (9 s t ) 4  J 9 (  )[cos M cos (9 s t )  sin M sin (9 s t )] 2 (15)  J1 ( ) J 9 (  ){sin[ (9 s   IF )t ]  sin[ (9 s   IF )t ]}} Taking fs  6.5GHz, fIF  1.5GHz, f9  58.5GHz, Simulation has... such as video, multimedia and other new value-added services In order to offer these broadband services, wireless systems will need to offer higher data transmission capacities Fig 1 Global growth of mobile and wireline subscribers 244 Microwave and Millimeter Wave Technologies: Modern UWB antennas and equipment By increasing operating frequencies of wireless system, a broader bandwidth can be provided... fiber-optic links, which exploit the advantages of both optical fibers and mm -wave frequencies to realize broadband communication systems and contribute a lot to the development of mmwave Radio over Fiber (RoF) systems (Sun et al., 199 6; Braun et al., 199 8; Kitayama, 199 8) Figure 2 gives the architecture of mm -wave RoF system Central Station (CS) and distributed Base Stations (BS) are linked with optical fibers... Handbook (2nd Ed.), Artech House Inc., ISBN 97 8158053 690 5, Norwood, MA M Skolnik, G Nemhauser, and J Sherman ( 196 4) Dynamic programming applied to unequally spaced arrays, IEEE Transactions on Antennas and Propagation, Vol AP-12, No 1, (Jan 196 4) 35-43, ISSN 1045 -92 43 H Unz ( 196 0) Linear arrays with arbitrarily distributed elements, IRE Transactions on Antennas and Propagation, Vol 8, No 2, (Mar 196 0)... O, (f) Waveform of demodulated 100-Mbps Ethernet data 254 Microwave and Millimeter Wave Technologies: Modern UWB antennas and equipment It is expected that strong 40-GHz mm -wave will be generated at PD in BS This is proved by the RF spectrum at PD output, as shown in Figure 10 (a) where 40-GHz peak is the highest among other harmonics and odd harmonics disappear, because the bias voltage has been adjusted... Vol 8, No 2, (Mar 196 0) 222-223, ISSN 0 096 - 197 3 B Van Veen, and K Buckley ( 198 8) Beamforming: A Versatile approach to Spatial Filtering, IEEE ASSP Magazine, (Apr 198 8) 4-24 Millimeter- wave Radio over Fiber System for Broadband Wireless Communication 243 13 x Millimeter- wave Radio over Fiber System for Broadband Wireless Communication Haoshuo Chen, Rujian Lin and Jiajun Ye Shanghai University, Shanghai . Propagation, Vol. 9, No. 2, (Mar. 196 1) 187- 192 , ISSN 0 096 - 197 3 Microwave and Millimeter Wave Technologies: Modern UWB antennas and equipment 242 R. Haupt ( 199 4). Thinned arrays using genetic. mobile and wireline subscribers. 13 Microwave and Millimeter Wave Technologies: Modern UWB antennas and equipment 244 By increasing operating frequencies of wireless system, a broader bandwidth. generating mm -wave signal by using MZM (O'Rcilly et al., 199 2). Microwave and Millimeter Wave Technologies: Modern UWB antennas and equipment 246 Fig. 4. The usage of MZM as external modulator.